Automatically Proving Plane Geometry Theorems Stated by Text and Diagram

Abstract

This paper presents an algorithm for proving plane geometry theorems stated by text and diagram in a complementary way. The problem of proving plane geometry theorems involves two challenging subtasks, being theorem understanding and theorem proving. This paper proposes to consider theorem understanding as a problem of extracting relations from text and diagram. A syntax–semantics (S2) model method is proposed to extract the geometric relations from theorem text, and a diagram mining method is proposed to extract geometry relations from diagram. Then, a procedure is developed to obtain a set of relations that is consistent with the given theorem with high confidence. Finally, theorem proving is conducted by using the existing proving methods which take the extracted geometric relations as input. The experimental results show that the proposed theorem proving algorithm can prove 86% of plane geometry theorems in the test dataset of 200 theorems, which is all the theorems in the popular textbook. The proposed algorithm outperforms the existing algorithms mainly because it can extract relations not only from text but also from diagram.